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arXiv · 0908.0577

Form-Type Calabi-Yau Equations

Jixiang Fu·Zhizhang Wang·Damin Wu
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Abstract

Motivated from mathematical aspects of the superstring theory, we introduce a new equation on a balanced, hermitian manifold, with zero first Chern class. Solving the equation, one will obtain, in each Bott--Chern cohomology class, a balanced metric which is hermitian Ricci--flat. This can be viewed as a differential form level generalization of the classical Calabi--Yau equation. We establish the existence and uniqueness of the equation on complex tori, and prove certain uniqueness and openness on a general K\"ahler manifold.

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Jixiang Fu, Zhizhang Wang, Damin Wu. 2009-08-05. Form-Type Calabi-Yau Equations. https://arxiv.org/abs/0908.0577

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